Cooperative binding: a multiple personality.

Cooperative binding has been described in many publications and has been related to or defined by several different properties of the binding behavior of the ligand to the target molecule. In addition to the commonly used Hill coefficient, other characteristics such as a sigmoidal shape of the overall titration curve in a linear plot, a change of ligand affinity of the other binding sites when a site of the target molecule becomes occupied, or complex roots of the binding polynomial have been used to define or to quantify cooperative binding. In this work, we analyze how the different properties are related in the most general model for binding curves based on the grand canonical partition function and present several examples which highlight differences between the cooperativity characterizing properties which are discussed. Our results mainly show that among the presented definitions there are not two which fully coincide. Moreover, this work poses the question whether it can make sense to distinguish between positive and negative cooperativity based on the macroscopic binding isotherm only. This article shall emphasize that scientists who investigate cooperative effects in biological systems could help avoiding misunderstandings by stating clearly which kind of cooperativity they discuss.